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The helicopter’s footage was meant to be an archival record of the skyline.

The resultant film from Catherine Yass, a video artist, was entered for the Turner prize and was supposed to “capture our desire to fly”.

One critic, however, said the loop-the-loop camera work captured only his desire to vomit.

The new complex is meant to house all radio, news and World Service broadcasts when it is completed in 2012. It is already three years late and £20m over budget.

The BBC said it was forced to provide public art as part of its planning permission for the redevelopment from Westminster council.

Philip Davies, a Tory member of the Commons culture, media and sport select committee, told the Sunday Times: “The BBC do not live in the real world. This kind of largesse would be unthinkable to any other organisation in the public sector.

“I favour top-slicing the BBC’s licence fee income and handing the money to commercial broadcasters to do something to serve the public. It is better than spending tens of thousands of pounds satisfying Alan Yentob’s art preferences.”

Brian Sewell, the art critic, added: “I do not think in hard-pressed times like this the BBC should fork out money for artists. It is not their business. Why are they doing it? It comes out of the licence fee. “It infuriates me that Alan Yentob has any say in the matter. He is now the most important critic in the country.”

A spokesman for the BBC said: "Part of the mandatory planning permission requirements for the redevelopment of Broadcasting House by Westminster City Council in 2003 were that the BBC invested in a public art programme.

"The plan for this art programme was approved by the Council's Public Art Advisory Committee, and then each individual artwork was subject to consultation and approval."